Details about Gulen's personal life and his ties to those ventures have long been murky, giving rise to suspicions about his motives.

Some of the U.S. schools have been investigated by the FBI due to financial mismanagement and visa fraud allegations.

One of the most explosive claims is that the schools are importing Turkish teachers to identify impressionable students and indoctrinate them into Gulen's movement, sometimes called Hizmet, Turkish for 'service'.

Nobody associated with the U.S. schools has been charged, and there has been no public outcry from parents or students about teachers promoting Islam, Gulen's supporters say.

In America, the schools are public and open to students of all faiths.

'Try proselytizing evangelical Christians in the center of Texas. See what happens.

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Mr Gulen leaves the Pennsylvania compound (pictured) to go to the doctor for his heart disease and diabetes

Mr Gulen said he is not worried about the U.S. government forcing him to leave the Golden Generation Worship & Retreat Center (pictured) to go back to Turkey to stand trial

His supporters started 1,000 schools in more than 100 countries.

In Turkey, they have run universities, hospitals, charities, a bank and a large media empire with newspapers and radio and TV stations.

Gulen's reach is shrouded in such mystery that Loyola University Maryland sociologist Joshua Hendrick, who has studied and written about him, estimates his following at anywhere from 500,000 to four million people.

'I think deep down in the hearts of these people, they want to create a better world, a world of peace, a world of respect.

'I saw no indication they are after power or creating any kind of (Islamic) state,' said University of Houston sociologist Helen Rose Ebaugh, who traveled the world studying the Gulen movement's finances and aims.

Turkey's government has branded the movement a 'terror organization,' though it is not known to have committed any acts of violence.

'The grain of truth, which we don't deny, is that yes, there are some sympathizers in every government institution. But to claim that there is a parallel entity, or there is a mastermind or puppeteer, is simply an empty claim,' Mr Aslandogan said.